Lord Justice Leveson said the press had "wreaked havoc in the lives of innocent people" for many decades.
But the report's recommendations have divided the coalition government.
David Cameron said he had "serious concerns" over statutory
regulation but Nick Clegg said he supported some form of legal
underpinning.
And Labour leader Ed Miliband urged the government to accept the report in its entirety.
Speaking in the Commons, Mr Cameron said he broadly welcomed Lord Justice Leveson's principles to change the current system.
But he said: "We should be wary of any legislation that has the potential to infringe free speech and the free press.
"The danger is that this would create a vehicle for
politicians whether today or some time in the future to impose
regulation and obligations on the press."

Deputy Leader Nick Clegg said
changing the law was the only way to ensure "the new regulator isn't
just independent for a few months or years, but is independent for
good".

Mr Miliband described the report as "measured, reasonable and
proportionate" and said Labour "unequivocally" endorsed its
conclusions.
After the first of cross-party talks, a senior Labour source
said Mr Cameron had agreed to ask the Department for Culture, Media and
Sport (DCMS) to draft a bill to implement Lord Justice Leveson's
recommendations.
The source added Labour would push for a Commons vote on implementing the recommendation in principle by the end of January.
The Hacked Off campaign, which represents victims of phone
hacking said Mr Cameron's "failure" to accept the full recommendations
of the report was "unfortunate and regrettable". Continue reading the main story

Founder Brian Cathcart said:
"Despite their years of abuses and outrageous conduct, it seems that the
prime minister still trusts the editors and proprietors to behave
themselves. It seems that the prime minister wants self-regulation all
over again."

Madeleine McCann's mother Kate said she hoped the report
would "mark the start of a new era" for the press, in which it treated
those in the news "with care and consideration".

Bob Satchwell, executive director
of the Society of Editors said he hoped any British politician would
hesitate before doing anything that "might in the slightest way threaten
the freedom of the media".

"What happens 20 years down the line if you have a different
government, which was upset by the press again, once you've given away
the principle and put a law in place, it's very easy to amend."
Mr Cameron set up the Leveson Inquiry in July 2011 after it
emerged journalists working for the Sunday tabloid the News of the World
had hacked the mobile phone of murdered Surrey schoolgirl Milly Dowler.
The paper was subsequently shut down by its owners News International.'Accountable press'
Among Lord Justice Leveson's findings:

All of the press served the country "very well for the vast majority of the time"

The press must create a new and tough regulator backed by legislation to ensure it was effective

Over last 30 years all political parties have had too close a
relationship with the press which has not been in the public interest

Former Culture Secretary Jeremy Hunt was not biased in his
handling of News Corp's BSkyB bid but failed to supervise his special
adviser properly

The tabloid press often failed to show "consistent respect for
the dignity and equality of women", and there is a "tendency to
sexualise and demean" women.

In his 2,000-page report, Appeal Court judge Lord
Justice Leveson said his proposals will protect the rights of victims
and people bringing complaints.
He said the press had failed to properly regulate itself in
the past, but he believed the law could be used to "validate" a new
body.

Analysis

Clive ColemanBBC News legal correspondent

The statute proposed by Lord Justice Leveson is intended to do
three things: Enshrine freedom of the press for the first time;
recognise the new regulator; and ensure it can be can be audited to
confirm it is performing to proper standards.
It also provides incentives to publishers to sign up.
Incentives are needed because no serving newspaper editor can serve on
the new body. The proposals amount to the press being allowed to set up
its own regulator, but not sit on it.
Principally the incentives involve setting up an arbitration
service to settle disputes with members of the public over privacy and
libel. If a publisher isn't part of that service and has to go to court,
it could be deprived of very considerable legal costs, even if it won.
And if it lost, it could be made to pay additional, exemplary damages.
These proposals on arbitration represent a very large carrot
and stick and that, says Lord Justice Leveson, needs legislation. But in
addition, there's a shotgun in the cupboard. The broadcast regulator
Ofcom could act as a backstop regulator for those publishers not
persuaded by the Leveson carrot and stick.

He said: "There have been too
many times when, chasing the story, parts of the press have acted as if
its own code, which it wrote, simply did not exist.

"This has caused real hardship, and on occasion, wreaked
havoc with the lives of innocent people whose rights and liberties have
been disdained.
"This is not just the famous but ordinary members of the
public, caught up in events (many of them truly tragic) far larger than
they could cope with but made much, much worse by press behaviour that,
at times, can only be described as outrageous."
Lord Justice Leveson said putting "a policeman in every
newsroom is no sort of answer," because legal powers were limited to
allow the press to act in the public interest.
However, the press is "still the industry marking its own
homework", and needs an independent self-regulatory body to promote high
standards, he added.
The Metropolitan Police said it accepted the criticisms made against it in the report.
Commissioner Bernard Hogan-Howe said he had already taken
"decisive action" on the issues raised and his priority was now ensuring
phone-hacking victims got justice.
The chairman of the Press Complaints Commission, Lord Hunt,
said the press had to seize the baton and make sure it "doesn't let Lord
Justice Leveson down".